Arbitrary Fiber Orientation Research Articles

Stress Singularity of Edge Delamination in Angle-Ply and Cross-Ply Laminates

By utilizing the general solutions derived for the plies with arbitrary fiber orientations under uniform axial strain (Huang and Chen, 1994), the explicit solutions of the edge-delamination stress singularities for the angle-ply and cross-ply laminates are obtained. The dominant edge-delamination stress singularities for the angle-ply laminates are found to be a real constant, −1/2, and a pair of complex conjugates, −1/2±i/2πln{(b+b2−a2)/a}. For the cross-ply laminates, the significant effect of transverse shear stresses of the laminate is considered and the dominant edge-delamination stress singularities are shown as −1/2 and −1/2±i/2πln{(c2+c22−4c1c3)/2c1}. a, b, cl, c2, and c3 are the corresponding combined complex constants. In addition, two elementary forms of edge-delamination stress singularity, say, r−1/2 and rδr(lnr)n(δr=n−3/2,n=1,2...) exist for both the angle-ply and cross-ply laminates. Excellent correlations between the present results and available solutions show the validity of the approach. The deficiencies of the solutions available in the literature are compensated. New results for other angle-ply and cross-ply laminates are also provided.

A finite volume model of cardiac propagation

This paper describes a two-dimensional cardiac propagation model based on the finite volume method (FVM). This technique, originally derived and applied within the filed of computational fluid dynamics, is well suited to the investigation of conduction in cardiac electrophysiology. Specifically, the FVM permits the consideration of propagation in a realistic structure, subject to arbitrary fiber orientations and regionally defined properties. In this application of the FVM, an arbitrarily shaped domain is decomposed into a set of constitutive quadrilaterals. Calculations are performed in a computational space, in which the quadrilaterals are all represented simply as squares. Results are related to their physical-space equivalents by means of a transformation matrix. The method is applied to a number of cases. First, large-scale propagation is considered, in which a magnetic resonance-imaged cardiac cross-section serves as the governing geometry. Next, conduction is examined in the presence of an isthmus formed by the microvasculature in a slice of papillary muscle tissue. Under ischemic conditions, the safety factor for propagation is seen to be related to orientation of the fibers within the isthmus. Finally, conduction is studied in the presence of an inexcitable obstacle and a curved fiber field. This example illustrates the dramatic influence of the complex orientation of the fibers on the resulting activation pattern. The FVM provides a means of accurately modeling the cardiac structure and can help bridge the gap between computation and experiment in cardiac electrophysiology.

On the free-edge stress singularity of general composite laminates under uniform axial strain

This work presents a rigorous study on the free-edge stress singularity for general composite laminates (except the angle-ply and cross-ply laminates) under uniform axial strain. Based on the general solutions derived for the plies with 0°, 90° and arbitrary fiber orientations, the corresponding transcendental characteristic equations of general [θ1/θ2], [θ/0°] and [θ/90°] laminates are established by using appropriate near-field boundary conditions, respectively. To avoid numerical errors, the transcendental characteristic equations are expanded by a symbolic operation technique analytically and solved graphically. Hence, once the ply material properties and stacking sequence are known, the accurate characteristics of the free-edge stress singularity of examined composite laminates can be obtained. These will be helpful for the failure analysis of composite materials and structures.

Multilayer hybrid-stress finite element analysis of composite laminate with through-thickness cracks

An assumed hybrid-stress finite element model using a simple composite multilayer element is developed to analyze generally thin or moderately thick composite laminates with through-thickness cracks. The assumed stress field satisfies: (i) equilibrium conditions within each layer, (ii) the traction reciprocity conditions at interlaminar boundaries, and (iii) the traction-free boundary conditions at the top and bottom faces of the laminate. Since the number of nodes and assumed stress parameters are independent of the number of layers, the multilayer element devised is quite effective especially for the laminate with a large number of layers. Several selected composite laminates with a through-thickness edge crack are solved. Many fewer degrees of freedom and only a one-step solution are necessary for the present technique. The variations of mixed-mode stress intensity factors across the thickness of the composite laminate are also computed. Excellent agreements between the present results and referenced solutions are drawn. The technique developed is also applicable to analyze the structural behaviors of the cracked laminate with arbitrary fiber orientation and stacking sequence for which the stress singularity has not yet been found.

Equations of Elastic Deformation of Laminated Composite Shallow Shells

Shallow shells of laminated composite materials are being increasingly used in structural applications. A complete and consistent theory is needed to deal with elastic deformation problems (i.e., static deflections and stresses, free and forced vibrations). The present work develops equations of motion, which may be solved either exactly or by an approximate method (e.g., Galerkin, finite differences) and energy functionals which may be used with the Ritz or finite element methods to obtain approximate solutions. The equations are developed in terms of arbitrarily-oriented (i.e., nonprincipal) shell coordinates, including twist as well as radii of curvature. The equations account for arbitrary layer thicknesses, fiber orientations, and stacking sequences. Shear deformation and rotary inertia effects are neglected.

Inelastic Deformation and Fracture of Laminated Graphite/Epoxy Tubes under Multiaxial Stress States.

The mechanical behavior of laminated graphite/epoxy tubes under multiaxial monotonic loadings was elucidated with special emphasis on the effects of fiber orientation, loading condition and laminate structure. Tubular specimens of symmetrically laminated graphite/epoxy of 5 different fiber orientations θ (the angle of fiber measured from the specimen axis) were tested under monotonic combined tension/compression and torsion. Based on the preliminary results of the proceeding paper, the angle θ was specified to be 0°, ±22.5°, ±45°, ±67.5°and ±78.75°. The results on the stress-strain relationships and fracture stress loci were presented. It was shown that stiffness and strength decreased with an increase in the deviation of fiber orientation from the direction of principal stress, and the Tsai-Wu criterion applied very well. The theory which accounts for the fracture loci of arbitrary fiber orientations will be a future objective of research.

Stiffness and thermal expansion predictions for hybrid short fiber composites

AbstractA model is developed to predict thermal expansion coefficients and elastic moduli of multi‐component (hybrid) composites. The model includes the influences of fiber aspect ratio; isotropic and anisotropic fiber materials; planar, three‐dimensional or arbitrary fiber orientation; hollow and solid spherical reinforcements; and voids. The first step in the procedure is to predict the properties of an aligned‐fiber single‐reinforcement composite for each reinforcement type. Various micro‐mechanics approaches are used, depending on the type of reinforcement. A simplified version of Lee and Westmann's theory is found to work well for hollow spherical reinforcements. Performing an orientation average accounts for the spatial orientation of each reinforcement, then an aggregate averaging procedure combines the single‐reinforcement properties to model the hybrid. Predictions of the model compare favorably to experimental elastic and thermal properties of short fiber/hollow sphere composites designed for very high speed integrated circuit (VHSIC) board applications.

Prediction of mode I fracture toughness of unidirectional fibre composites with arbitrary crack fibre orientation from its lowest or matrix fracture tougness

Prediction of mode I fracture toughness of unidirectional fibre composites with arbitrary crack fibre orientation from its lowest or matrix fracture tougness

The effect of fiber orientation on the abrasive wear behavior of polymer composite materials

The effect of fiber orientation on the dry abrasive-dominant wear behavior of continuous-carbon-fiber-reinforced polyetheretherketone (CF-PK) and continuous-aramid-fiber-reinforced epoxy (K49/3501-6) was investigated. A pin-on-flat type test apparatus was employed in determining the wear rates as a function of fiber orientation for the two materials. Different wear rate distributions were found for each material, although the optimum wear resistance occurred when the fibers were oriented normal to the sliding surface in each case. The influence of fiber-abrasive particle interactions on the wear rate distribution is discussed with regard to microscopic observations of the worn surfaces. Lastly, the wear rate distributions are described empirically allowing the prediction of the wear rate at any arbitrary fiber orientation.

Effect of fibre orientation on the vibration behaviour of orthotropic rectangular plates

The effect of fibre orientation on the fundamental frequency of thin rectangular/square orthotropic plates is studied using a high precision triangular orthotropic finite element. In the case of a square plate with a simply supported boundary condition, the fundamental frequency increases as the fibre orientation varies from 0 to 45° and decreases symmetrically from 45 to 90°. An opposite trend is observed in the case of a square plate with clamped boundary conditions. The element is useful in studying plates of arbitrary plan form and arbitrary fibre orientation.

The Slotted Tension Shear Test for Composite Laminates

The mechanical behavior of a composite laminate can be predicted by lamination theory if the properties of individual lamina are known. The in-plane shear stiffness and strength of lamina and of multidirectionally reinforced laminates have often proved to be most difficult to measure. In this article, we present an experimental technique that is used at Lockheed Missiles & Space Company, Inc., to measure the inplane shear properties of advanced composite laminates with plies of arbitrary fiber orientation.